Regression on hidden variables

[mareram]

I'm thinking about...

Imagine that I've got a set of variables I want to make regression on. But I can only observe other different set of variables . With not known and the being hidden variables.

I guess that I can make assumptions (which can be tested using validation later with different sets of ) about the form of the functions f and then derive certain nonlinear transformations that correspond to those f and which relate the x's and the y's.

Then I can make nonlinear regression to the x's. But it seems a bit twisted since I'm applying nonlinear transformations twice.

does anyone know about a particular theory on machine learning that copes with this kind of problems? Or simply what I should do is considering a set of nonlinear transformations big enough so that it contains the transformations needed for adjusting to and to transform them later to the ?

Thanks a lot

[palmipede]

Life is much easier if the f's are known and linear. If they are not known but linear that is an estimation problem. I'd start looking for Gaussian state-space models or linear dynamical systems.